Special unitary group
In abstract algebra
, the special unitary group
of degree n
over a field F
(written as SU(n
)) is the group
by n unitary matrices
1 and entries from F
, with the group operation that of matrix multiplication
. This is a subgroup
of the unitary group
), itself a subgroup
of the general linear group
If the field F is the field of real or complex numbers, then the special unitary group SU(n,F) is a Lie group.
A common matrix representation of the generatorss of SU(2) is:
( is the square root of -1.)
This representation is often used in quantum mechanics
to represent the spin
of fundamental particles such as electrons
. They also serve as unit vectors for the description of our 3 spatial dimensions in quantum relativity.
Note that the product of any two different generators is another generator, and that the generators anticommute. Together with the identity matrix,
these are also the generators of U(2). These 4 matrices then form a complete set on 2x2 matrices.